Surface Area of a Cylinder

Remember the formulas for the lateral surface area of a prism is
p
h
and the total surface area is
p
h
+
2
B
. Since the base of a cylinder is a circle, we substitute
2
π
r
for
p
and
π
r
2
for
B
where
r
is the radius of the base of the cylinder.

So, the formula for the
lateral surface area
of a cylinder is
L
.
S
.
A
.
=
2
π
r
h
.

Example 1:

Find the lateral surface area of a cylinder with a base radius of
3
inches and a height of
9
inches.

L
.
S
.
A
.
=
2
π
(
3
)
(
9
)
=
54
π
inches
2

≈
169.64
inches
2

The general formula for the
total surface area
of a cylinder is
T
.
S
.
A
.
=
2
π
r
h
+
2
π
r
2
.

Example 2:

Find the total surface area of a cylinder with a base radius of
5
inches and a height of
7
inches.